Mark Davis Will Not Return to San Diego : Padres: Final session to keep Cy Young Award winner goes nowhere. Team signs Lefferts as left-handed stopper.

There was one last-ditch negotiating session Thursday, but when Jack McKeon hung up the telephone in his hotel suite, he said it officially is over.

Mark Davis, the 1989 free-agent Cy Young reliever who saved 44 games, no longer is wanted by the San Diego Padres.

“We’re out of the free-agent business,” said McKeon, manager and vice president of baseball operations for the Padres. “There are no hard feelings. He was looking out for his best interest, and I was looking out for mine. We gave him every chance in the world, and he didn’t take it.”

McKeon added: “Our left-handed stopper now is Craig Lefferts.”

Lefferts, who had a career-high 20 saves for the San Francisco Giants this season, signed a three-year, $5.4-million contract Thursday.

He will share the stopper’s role with right-hander Greg Harris, who has six saves in his career.

Davis and his agents, Alan and Randy Hendricks, Monday night rejected the Padres’ final offer of four years for $12 million. Davis insisted on a five-year contract. Padre owner Joan Kroc insisted on four.

“She’s made it clear that it’s over,” McKeon said, “so we’ve just got to go on.”

Davis, who has not returned telephone calls for the past two weeks, must decide where to take his services. He already has five-year guaranteed contracts awaiting him from the Montreal Expos, New York Yankees and Philadelphia Phillies. And who knows? The Angels just might be in this hunt.

The termination of Davis’ career in San Diego culminates nine months of botched negotiations. Davis offered to sign a two-year extension for $2.8 million this spring, and sources said he would have signed for as little as $2.4 million. But Padre President Dick Freeman refused to budge from his $2.2 million counteroffer.

There were no negotiations again until the end of the season. The Padres then made four offers: three years for $5 million; three years for $5.4 million; three years for $6.9 million, and finally, four years for $12 million.

As soon as free-agent starter Mark Langston signed a five-year, $16-million contract with the Angels, Davis demanded a five-year contract exceeding Langston’s.

With negotiations at a stalemate, Kroc put McKeon in charge of all baseball operations Sunday. He met for about an hour Monday with the Hendricks brothers, and the next time they talked on Thursday, the agents asked McKeon to reconsider, to no avail.